Pumps of the aforedescribed type are used for instance in power-assisted steering systems and feed a special fluid, e.g. an oil, for assistance of the steering forces exerted on the steering wheel of a motor vehicle. Preferably these pumps are vane pumps, which suck oil from a supply outside the pump, such as a reservoir. Such pumps are equipped with a valve, i.e. a flow control valve, through which the oil can be directed from the, high pressure region to the suction region of the pump. Starting from a certain rotational speed of the pump and at firmly established flow rates the valve opens an escape bore, wherein the oil under high pressure can escape. The bypassed oil reaches the intake space of the delivery system. Frequently the pump is not completely filled with the hydraulic oil. Moreover the channels through which the oil flows can be damaged due to cavitation.